396 I C allege & Research Libraries • September 1982

MODMEKKAWI

In May of 1980 the Association of Research Libraries (ARL) adopted new criteria for membership in the association based, in large part, on what is known as the ARL Li-brary Index. 1 This index is derived from a model containing ten categories, or varia-bles, which characterize library size.

While the Library Index model was devel-oped as a measure of an institution's overall standing relative to the ARL membership, this author has found it to be useful, if prop-erly employed, as a decision-making tool in short-term planning, programming, and budgeting in those operations affecting li-brary size. This article describes the proce-dure for this application of the index.

WHAT Is THE LIBRARY INDEX?

Until 1980, ARL Statistics described the size and rank of ARL member institutions separately in terms of holdings, expendi-tures, staffing, and interlibrary loan activ-ity. While the institutions could be compared on these variables, one at a time, there was no summary measure of an institution's over-all ranking in the association. The ARL model was designed to provide such a sum-mary characterization.

The model is as follows:

EFSC; (log k; - log K;) I s.d. K;

where, in a given year: FSC; Factor score coefficient of variable i; k; Value of variable i for the study institu-

tion; Mean of variable i; Standard deviation of variable i.

The ten variables included in the model are defined as:

1. Volumes held, excluding microforms and government documents;

2. Volumes added (gross) , excluding mi-

Mod Mekkawi is architecture and planning li-brarian, Howard University, Washington, D.C.

The ARL Library Index as a Decision-Making Tool

croforms and government documents; 3. Microforms held, inCluding micro-

film reels, microcards, microprints sheets, microfiches;

4. Current serials received, including periodicals;

5. Expenditures for library materials, including books and serials;

6. Expenditures for binding; 7. Expenditures for salaries and wages,

including student assistants' wages, but omitting fringe benefits;

8. Other operating expenditures; 9. Number of FTE professional staff;

and 10. Number of FTE nonprofessional

staff. Thus for XYZ university library (a hypo-

thetical institution) , the index score will be calculated by substitution of the variables in the model with their corresponding values for this library. Using the 1979/80 ARL model, we calculate XYZ's index as shown in table 1. As it turns out, some of the calculated component scores are negative, which indi-cates areas in need of improvement if XYZ in-stitution wishes to score higher in ARL.

Given certain characteristics of the ARL model and the current conditions at XYZ, how can this institution achieve a certain im-proved index score most economically? Note that in 1979/80, the scores of the ARL mem-bers ranged from a low of - 1. 93 ( 0 klahoma State) to a high of + 3.00 (Harvard), with - .38 for the university median.

MANAGEMENT APPLICATION OF THE ARL MODEL

The library administration will set a goal to achieve a certain index score within a given time framework-for instance, one year. Given the library's current component values, its costs of increasing each indepen-dent variable (book, serial, microform) by one unit, the costs of increasing the depen-

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Research Notes I 397

TABLE 1

PROCEDURE FOR CALCULATING THE LIBRARY INDEX, XYZ UNIVERSITY LIBRARY, 1979/80 Component Variable FSC; k;

1. VOLHELD .12108 rog 1116396 2. VOLADDED .11940 log 57902 3. MICFORM .07509 log 1165076 4. CT SERIALS .12253 log 13156 5. MAT EXPEND .12553 (log 1894321 6. BINDING .11266 ~log 34132 7. TTL SALARIES .12581 log 3609365 8. OPER EXPEND .10592 tg 625014 9. PROFSTAFF .12347 log 83

10. NONPROF .12970 log 124 Total score (Library Index)

dent variables (materials expenditures, bind-ing, salaries and wages, other operating ex-penditures) caused by one unit increase in the dependent variables, and the weight of the dependent and independent variables in the ARL model, one can apply linear program-ming principles to find the best use of the li-brary's resources.

Because this problem involves not only product mixing (books/serials/microforms) , but also changes in the dependent compo-nents as the products are increased in certain ratios and quantities, formal linear program-ming techniques can be unnecessarily com-plex. The author has therefore worked out a shortcut procedure that may well yield the optimization effect sought in a formal linear programming solution.

Before looking at the procedure, let us state the major requirements of the problem:

1. There must be an objective the library wants to achieve. Obviously, its major objec-tive, in terms of ARL standing, is to maxi-mize the total contribution of the compo-nents in the ARL model. The component contributions, or scores, add up to the Li-brary Index.

2. There must be alternative courses of action, one of which will achieve the above objective. In what ratio should the library in-crease its book/ serial resources-!: 1? 3: 1? 0:1? Some other ratio?

3. Dollar resources are limited. One serial may cost twice as much as one book. Conse-quently, the more money that is spent on se-rials, the less there will be to spend on addi-tional books .

4. The ratio of book:serial and the amount of books and/or serials additions needed to achieve the objective (a target

s.d. Component K; K; Score

- 6.2916) .2172 -0.135897 - 4.8412) .2025 -0.046290 - 6.0950) .1763 -0.012200 - 4.3432) .2341 -0.117283 - 6.2333) .1636 0.033879 -5.0480) .2475 -0.234350 - 6.4675) .2103 0.053801 - 5.6773) .2635 0.047670 -1.8281) .1968 0.057079 - 2.1512) .2046 -0.031902

-0.385493

ARL score) depend (beside costs and propor-tion of serial subscriptions going into the col-lection as volumes added) on the component score coefficients, or weights, in the ARL Li-brary Index model.

PROCEDURE

The computational routine is an iterative process. In working toward the target score, the routine is repeated over and over, in a sys-tematic pattern, until the preestablished score value has been reached.

Of the three independent variables in the model-books, current serials received, and microforms-we shall use, to simplify the problem, two "products" only, namely books and serials. In what ratio should these vari-ables be increased?

Assume lower and upper limits of 0 and 9 for either element in the relation. That is, in the extreme cases, the book:serial ratio can be 0:9 or 9:0. There are fifty-seven alterna-tive exclusive ratio combinations: 0:1, 1:0, 1:1, 1:2, 1:3, etc.

Assume also that all new serial additions are bound and added to the collection, and that one serial title produces one bound vol-ume on the average. Thus, increasing books and serials by one unit each (1:1 ratio) will increase volumes added and volumes held by twounitseach. Similarly, a4:1 ratio will in-crease volumes added and volumes held by five units each.

At the same time, expenditures for materi-als, binding, total salaries, other operating items, and the quantity of manpower needed to carry the additional work loads, are all in-creased by appropriate amounts for each one serial or monographic addition. These amounts are displayed in table 2. 2

398 I College & Research Libraries • September 1982

TABLE 2

INPUT DATA CAUSED BY ADDITION OF ONE MoNOGRAPHIC oR SERIAL UNIT

TO THE COLLECTION

Component Item Additional Unit Variable Added Cost per Item

MAT EXPEND Book $25.0 Serial 50.0

BINDING Book 0.0 Serial 7 .0

SALARIES Book 20.0 Serial 23.0

PROF STAFF Book .00059 m~nyear Serial . 00059 manyear

NONPROF Book .00073 manyear Serial .00093 manyear

ote: The personnel and salaries data are based on (1) known work-load factors for library operations and (2) estimated annual salaries and wages of $20 ,000 and $12,000 for professionals and nonprofessionals, respectively.

Before we begin the computations, we must adjust the basic data for XYZ by adding initially to its VOLHELD a quantity equal to the number of volumes added in 1979/80. The assumption here is that XYZ will add to its collection in the projected year, books and serials in the proportions and quantities re-ported in the previous year. All other addi-tions, needed to improve the index score, will be over and above the initial increments. The rate of serial binding is again assumed to be 100 percent. Thus, for XYZ, the value of vol-umes at the start of the computational rou-tine is 1174396 (1116396 + 58000).

Using the adjusted statistics and the input data from table 2, the PL/ 1 program given in appendix 1 develops solutions to this prob-lem. For each of the eleven ARL target scores, ranging from 0 to 1.0, the program

produced fifty-seven tables, a sample of which is given in table 3. The optimal solu-tion for each target score is that that corre-sponds to the lowest amount of total addi-tional expenditures shown at the foot of each table. The book: serial ratio can be easily de-termined from the input data printed above the table, where the second item represents volumes added (monographs plus serials) , and the third item units of serials added in each loop.· Hence, the book:serial ratio in ta-ble 3 is 1:3 .

For XYZ library, the optimal book:serial ratio is 0:1 for each of the eleven alternative score targets: that is , if a certain target score were to be achieved most economically, all additional funds would have to be allocated to increasing the number of current serials received, while book additions remained at the previous level.

What if the proportion of additional seri-als that are bound into volumes was less than 100 percent? Table 4 shows that the book: se-rial ratio of 0:1 remains the optimal product mix at every rate of binding except zero, that is, when none of the additional serial titles is bound at year's end. At the same time, the cost of achieving the given target score in-creased as the rate of binding dropped from one to zero. Except for binding expenditures, which obviously decreased as the proportion of serials sent to bindery decreased, all the other expenditures increased as more serials had to be added to reach the same score. This observation is quite instructive. It indicates that a certain score can be reached less expen-sively when most, if not all , of the current se-

TABLE 3

SAMPLE REsouRCE ALLOCATION TABLE FOR IMPROVED INDEX ScoRE (LI = 0 .100000 DATA = 4 4 3 175 20 21)

Value Target Component Current Target Increase Score

VOLHELD 1174396 1184676 10280 -0.121520 VOLADDED 57902 68182 10280 -0.004434 MICROFORMS 1165076 1165076 0 -0.012201 CT SERIALS 13156 20866 7710 -0.012431 MAT EXPEND 1894321 2344071 449750 0.104875 BINDING 34132 88102 53970 - 0.046891 TOTAL SALARY 3609365 3839637 230272 0.069869 OPEREXPEND 625014 676414 51400 0.061470 PROF STAFF 83 89 6 0.076295 NONPROF 124 133 9 -0.015017

TOTAL 0 .100015 Total Additional Expenditures = 785392. Binding Rate = 1.0

rials received are bound and added as vol-umes to the collection. This is less costly than subscribing to an increasingly larger number of titles and discarding a large proportion of the hard copies at year's end in favor of (1) microfilm or (2) straight elimination as a lim-ited number Uust over 7 ,000) of currently published serials are available on microfilm.

CoNCLUSION

It has been shown how the ARL Library Index model can be used in a large-scale li-brary operation to:

1. Determine alternatives in the alloca-tion of additional funds and the total amount needed in each case to reach a certain im-proved ARL score;

2. Determine which combination of vari-ous library materials will produce the ex-pected outcome less expensively;

3. Identify the concomitant increases in staffing, salaries, binding, and other operat-ing costs; and

4. Identify the trade-offs between the op-timal solution and less efficient alternate so-lutions to achieve the established goal.

This information is especially valuable in a planning-budgeting process which uses Zero Base Budgeting (ZBB) techniques.

Obviously, the selection of a course of action is not altogether quantitative. The de-cision is often affected by issues that are not amenable to quantification. These issues re-late to the overall objectives of the institu-tion, its policy, or social values. Whereas the median ARL library spends about 55 percent of its materials budget on serials (with 80 per-cent for the ARL university high and 20 per-cent for the university low), a non-research-oriented institution need not, and indeed should not, follow the ARL pattern, which tends to focus on current serials acquisition. Similarly, an academic library that trails far behind comparable institutions in terms of monographic holdings would adopt a nonop-timal solution where the higher costs of de-veloping resources and achieving a certain measure of library size will be justified by the requirements of filling gaps in the book and microform collections.

A nonoptimal solution should also be fa-vored where space is a scarce resource; or where the flow of funds for library materials is erratic from year to year, for serial sub-

!-< <

Research Notes I 399

co t-"'

-400 I College & Research Libraries • September 1982

scriptions involve long-range financial com-mitment.

Nevertheless, the ARL model's usefulness in planning and budgeting is not seriously di-minished. It provides the library administra-tion with a scientific budgeting tool by iden-tifying alternative means of achieving an established objective and their associated costs.

REFERENCES

1. The Library Index is briefly explained in ARL Statistics, 1979-80 (Washington, D.C.: ARL, 1980) ; a full description of the index may be found in the ARL Library Index and Quantita-

tive Relationships in the ARL, a report by Ken-don Stubbs for the Committee on ARL Statistics (Washington, D .C . : ARL, 1980).

2. The cost factors shown in table 2 represent the actual costs at the XYZ institution. The work-load factors for library operations are calcu-lated from Robert M. Hayes and Joseph Becker, Handbook of Data Processing for Libraries (2d ed.; Los Angeles, Calif.: Melville Publ. Co. , 1974) , p .ll8. While the work-load factors are based on a "careful review of the literature and have been compared with the actual costs in several libraries as well as with a functional analysis of the operations themselves," the cost factors pertain to the XYZ institution and are used here for illustration only. The individual library must compare these rates with those re-ported by its own cost-accounting system.

APPENDIX 1: PL/I PROGRAM

The following PL/I program is used to develop alternative solutions to achieve an established Library Index score.

SCORES: PROC OPTIONS(MAIN); DCL X(2)FLOAT(l5), (Al,A2,A3,A4,AS,A6,A7,A8,A9,Al0,All,Al2,Al3,Al4,Al5,Al6,Al7,Al8,Al9,A20) FLOAT(lS), (k,L,M,N,P,Q,T,U,V)FLOAT(lS), (Sl,S2,S3,S4,SS,S6,S7,S8,S9,Sl0,Sll,Sl2,Sl3,Sl4,Sl5,Sl6,Sl7,Sl8,Sl9,S20,S21, S22,S23,S24,S25)FLOAT(l5), (R)FLOAT(lS); DCL (I,J,MAX) FIXED BIN(lS); MAX=2;

/* READ VALUE OF TARGET SCORE(S) */ DO I .. l TO MAX;

GET LIST (X(I)); END;

/* LIBRARY SIZE VALUES: Al, All• VOLHELD; A4, Al4• MATEXPEND; A7, Al7• BINDING; AlO, A20• NONPROF */

A2, Al2• VOLADDED; AS, Al5• OPEREXPEND; A8, AlB• TOTALSALARY;

A3, Al3• CT SERIAU; A6, Al6• MICROFO~ A9, Al9• PROFSTAFF;

All=ll74396; Al2•57902; Al3•13156; Al4•1894321; Al5•625014; Al6=1165076; Al7=34132~ Al8=3609365; Al9=83; A2Q=l24;

/* R• RATE OF SERIAL BINDING */ R=l; DO · I • l TO 57 ; Al•1174396; A2=57902; A3•13156; A4•189432l; A5=625014; A6•ll65076; A7•34132; A8•3609365; A9•83; Al0•124;

/* READ THE QUANTITIES TO BE ADDED IN EACH LOOP: K• BOOKS, BOUND SERIALS ADDED TO VOLHELD; L• BOOKS, BOUND SERIALS ADDED TO VOLADDED; M• SERIAL SUBSCRIPTIONS ADDED TO CT SERIALS; N• INCREASE IN MATEXPEND CAUSED BY THE ADDITIONAL BOOKS/SERIALS; P• INCREASE IN OPEREXPEND CAUSED BY THE ADDITIONAL BOOKS/SERIAL; Q= INCREASE IN BINDING EXPENDITURES CAUSED BY THE ADDITIONAL BO~S/

SERIALS; T• INCREASE IN TOTAL SALARIES CAUSED BY THE ADDITIONAL BOOKS/SE~ALS; U• INCREASE IN PROFESSIONAL STAFF CAUSED BY THE ADDITIONAL BOOKS/

SERIALS; V• INCREASE IN NON-PROFESSIONAL STAFF CAUSED BY THE ADDITIONAL BOOK5/

SERIALS */

Research Notes I 401

GET LIST (K,L,M,N,P,Q); T= ((L-M)*20.60)+(M*23.0); Ua ((L-M)* .00059)+(M*.00059); V= ((L-M)*.00073)+(M*.00093); K-K-M+ ( M*R) ; LaL-M+(M*R); Q•Q*R;

/* COMPUTE THE SOLUTIONS FOR EACH TARGET SCORE */ DO I • 1 TO MAX;

/* SET TABLE HEADING */ PUT EDIT ('LI .. ',X(I),' ;','DATA:',K,L,M,N,P,Q) (COL(1),A,COL(S),F(9,6),COL(16),A,COL(20),A,COL(25), 6 F(6)); PUT EDIT ( (60) '-') (COL(l) ,A); PUT EDIT ('VALUE')(COL(30),A); PUT EDIT ((31)'-' ,'TARGET' )(COL(l7),A,COL(53),A); PUT EDIT ('COMPONENT', 'CURRENT' ,'TARGET' ,'INCREASE' ,'SCORE')

(COL(1),A,COL(18),A,COL(29),A,COL(40),A,COL(53),A); PUT EDIT ( ( 60) I- I ) (COL (1) , A) ; Sllc 0;

/* COMPUTE LIBRARY INDEX AND TEST IF TARGET SCORE IS REACHED */ DO WHILE (511-> X(I));

A1aAl+K; A2•A2+L; A3•A3+M; A7•A7+Q; A8•A8+T; A9•A9+U; S1•.121079*(LOG10(Al)-6.29159)/.217199; S2 ... 119399*(LOG10(A2)-4.84119)/.202499; S3=.122529*(LOG10(A3)-4.34319)/.234099; s4s.l25529*(LOG10(A4)-6.23329)/.163599; S5=.105919*(LOG10(A5)-5.67729)/.263499; S6a.07509*(LOG10(A6)-6.0950)/.1763; S7•.11266*(LOG10(A7)-5.0480)/.2475; S8 ... 12581*(LOG10(A8)-6.4675)/.2103; S9a.12347*(LOG10(A9)-1.8281)/.1968; Sl0•.11297*(LOG10(Al0)-2.1512)/:2046; Sll= Sl+S2+S3+S4+SS+S6+S7+S8+S9+S10; END;

A4•A4+N; Al0•A10+V;

AS•AS+P;

/* COMPUTE THE AMOUNT OF INCREASE IN EACH COMPONENT VALUE, FROM CURRENT TO TARGET (IMPROVED) */

Sl2•Al-All; Sl7•A6-A16;

S13•A2-Al2; Sl4=A3-Al3;

Sl8•A7-Al7; S19•A8-Al8; S25 .. S15+Sl6+Sl8+Sl9;

S20•A9-Al9;

/* PRINT SOLUTION TABL~ */

S15=A4-AH; Sl6•AS-Al5;

S2l•Al0-A20;

PUT EDIT ('VOLHELD', A11,A1,Sl2,S1) (COL(1),A,COL(15),F(l0),COL(25),F(10),COL(36),F(l0),COL(50),F(l0,6)); PUT EDIT ('VOLADDED' ,A12,A2,Sl3,S2) (COL(l) ,A,COL(lS) ,F(lO) ,COL(25) ,F(lO) ,COL(36) ,F(10) ,COL( 50) ,F(l0,6)); PUT EDIT ('MICROFORM' ,A6,A16,Sl7,S6) (COL(1),A,COL(l5),F(10),COL(25),F(l0),COL(36),F(10),COL(50),F(l0,6)); PUT EDIT ('CT SERIALS' ,Al3,A3,Sl4,S3) (COL(1),A,COL(15),F(l0),COL(25),F(l0),COL(36),F(l0),COL(50),F(10,6)); PUT EDIT ('MATEXPEND' ,A14,A4,Sl5,S4) (COL(l) ,A,COL(lS) ,F(lO) ,COL(25) ,F(lO) ,COL(36) ,F(10) ,COL( SO) ,F(10,6)); PUT EDIT ('BINDING' ,A17,A7,S18,S7) (COL(1),A,COL(l5),F(10),COL(25),F(10),COL(36),F(l0),COL{50),F(l0,6)); PUT EDIT ('TOTALSALARY' ,Al8,A8,Sl9,S8) (COL(1),A,COL(15),F(10),COL(25),F(10),COL(36),F(l0),COL(50) 1F(l0,6)); PUT EDIT (I OPEREXPEND I ,AlS ,AS, 516 ISS ·) (COL(1),A 1COL(15),F(l0),COL(25),F(l0) 1COL(36) 1F(10),COL(50),F(l0,6)); PUT EDIT ('PROFSTAFF' I A19,A9,S201S9) (COL(1),A 1COL(15),F(l0) 1COL(25) 1F(l0),COL(36),F(10) 1COL(50) 1F(l0 16)); PUT EDIT ('NONPROF' I A20,A101S211S10) (COL (1) ,A I COL ( 15) IF ( 10) I COL ( 25), F ( 10), COL ( 36), F (10), COL (50) IF ( 10,6)); PUT EDIT ('TOTAL' ,Sl1)(COL(3),A,COL(50) 1F(10,6)); PUT EDIT ( ( 6 0 ) I - I ) ( COL (1 ) I A) ; PUT EDIT ('TOTAL ADDITIONAL EXPENDITURES .. ', S25, 'BINDING RATEa' 1 R)(COL(l), A , COL ( 3 2 ) , F ( 8 ) I COL ( 4 3 ) , A I COL ( 58 ) , F ( 2 , 1 ) ) ; PUT SKIP(2); END; END; END SCORES;

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